Question

One-quarter of the married couples in a distant society have no children at all. The other three quarters of families continue to have children until the first girl, and then cease childbearing. Assume that each child is equally likely to be a boy or girl.

a) For k=0,1,2,..., what is the probability that a particular husband will have k male offspring?

b) What is the probability that the husbands' male line of descent will cease to exist by the nth generation?

Answer #1

A married couple decides that they will continue to have
children until they have 3 boys. It is assumed that having a boy or
a girl is equally likely. (a) What is the probability that the
couple has 5 children until they have 3 boys? (b) How many children
does this couple expect to have until they have 3 boys?

A married couple decides that they will continue to have
children until they have 3 boys. It is assumed that having a boy or
a girl is equally likely. (a) What is the probability that the
couple has 5 children until they have 3 boys? (b) How many children
does this couple expect to have until they have 3 boys?
please show your work

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